Of course private wouldn't be the only option. Even with no FDA of any kind, laws against fraud, murder, etc, would still exist. Courts would still hear liability lawsuits, or torts, or what-have-you. As I've already mentioned, people often make the mistake of thinking that a lack of business-specific legislation means that corporations are then above the law. You seem to be making that mistake.
So far, you've said that the private sector has been mean to people in the past. Which is not persuasive, as governments have been worse.
The only other objection you've raised is the question of who would enforce truthfulness on the part of some privately-run FDA. To which the obvious response is, who enforces truthfulness on the part of the current FDA? Who is going to be easier to police or to sue, a government body, or a private organization? Wouldn't it be the latter? At best, isn't it a toss-up?